That's the way I register a Validator to my cells with the label "MonthEditLABEL". Now I need to add another validator on top of the same label, but if I do so the first validator seems to be overwritten.

Validator chains are currently not supported in NatTable. This is also not included in 1.0.0

What you could do is to create a validator that extends ContextualDataValidator. There you have the ConfigRegistry available and would be able to check for the whole LabelStack and check if there are additional validators registered. This allows you to create your own validator chain if necessary.